First, IRS Publication 523 Pub 523 talks about selling your home), page 10 states the general rule for non-community property state residents: "Surviving spouse. If you are a surviving spouse and you owned your home jointly, your basis in the home will change. The new basis for the interest your spouse owned will be its fair market value on the date of death (or alternate valuation date). The basis in your interest will remain the same. Your new basis in the home is the total of these two amounts." Simple, half of the house gets a date-of-death tax basis step up, the other half doesn't.
Then a few paragraphs later, it gives the rule for community property states, which is entirely different: " Community property. In community property states (including Arizona, California, Idaho, Louisiana, Nevada, New Mexico, Texas, Washington, and Wisconsin), each spouse is usually considered to own half of the community property. When either spouse dies, the total fair market value of the community property becomes the basis of the entire property, including the part belonging to the surviving spouse. For this rule to apply, at least half the value of the community property interest must be includible in the decedent's gross estate, whether or not the estate must file a return."
In Publication 555 (dealing with community property rules), they give an example of the community property tax basis step up rule: " Example. Bob and Ann owned community property that had a basis of $80,000. When Bob died, his and Ann's community property had an FMV of $100,000. One-half of the FMV of their community interest was includible in Bob's estate. The basis of Ann's half of the property is $50,000 after Bob died (half of the $100,000 FMV). The basis of the other half to Bob's heirs is also $50,000." My comment - and if Ann is Bob's heir, her tax basis is the full $ 100,000, even though only $ 50,000 was includible in Bob's estate.
So forget the MLP tax basis question for a moment and think about the house your mother and father owned. You said she's getting a basis step up for half of the house. If this was community property in a community property state, I think she gets a 100% step up. At least that is what the CA CPAs on my list serve are telling me. So talk to a CA accountant and see what they say before your mother sells the house.